Shakhtar Donetsk maintained a perfect record after four matches in Group J, leaving their third-placed French opponents battling to qualify with two matches still to play.
Luiz Adriano put the visitors ahead in the 50th minute and Oleksiy Gai doubled the lead 13 minutes later.
French side Toulouse were left three points behind second-placed Bruges after the Belgian club won 4-2 at Partizan Belgrade, who had Mladen Krstajic sent off for a second yellow card in the 79th minute after all the goals had been scored.
Athletic Bilbao failed to clinch a place after being held 1-1 away to bottom-placed Portuguese team Nacional, with Joseba Etxeberria's 85th-minute penalty earning a point for the Spanish side six minutes after the hosts had Nuno Pinto sent off for a second yellow card.
Werder Bremen also progressed into the knockout rounds after a 2-0 win at home to Austria Vienna saw the German side stay top of Group L and move eight points clear of their third-placed opponents.
Salzburg also maintained a perfect record in Group G with a 1-0 victory at 10-man Levski Sofia, but still need another point to progress.
Franz Schiemer scored a 90th-minute winner as the Bulgarians paid the price for having Georgi Sarmov sent off in the 62nd minute.
Villarreal kept their hopes alive with a 4-1 crushing of Lazio that saw the Spanish team go above the Italians on goal difference, with both on six points.
The hosts led 3-0 within 13 minutes as Robert Pires scored twice -- one from a long-range free-kick that eluded everyone and the other from the penalty spot --with Lazio's Roberto Baronio sent off in just the third minute.
Villarreal also had Gonzalo Rodriguez dismissed after 31 minutes, but Pasquale Foggia crashed the resulting penalty against the bar.
Mauro Zarate reduced the deficit on 73 but Giuseppe Rossi slotted home another penalty eight minutes from the end.
Benfica moved to the brink of qualification from Group I with a 2-0 victory away to English club Everton.
Javier Saviola and Oscar Cardoza followed up their doubles from the 5-0 victory at Goodison Park two weeks ago with a goal each in the second half to put the Portuguese side top on nine points.
Everton remained second on six points after AEK Athens and BATE Borisov were left on four points after a 2-2 draw in Greece which saw the Belarussian side hold on after having Igor Shitov sent off on 76 for a second booking.
Fenerbahce took another step to qualifying from Group H with a 3-1 win at home to Steaua Bucaresti which put the Turkish team two points clear of FC Twente.
Steve McClaren's Dutch side kept their hopes alive with a 2-1 win at home to Moldovan champions FC Sheriff, who are three points back in third place.